Why we should ditch 10

Yep, there are indeed numerous number nerds that believe we should get rid of the number 10. Now you are probably thinking…

What would make someone prejudiced against something as inoffensive and ordinary as a number? It seem like a pretty uncontroversial topic. Well, there is a passionate group of people known as dozenalists who believe we should replace 10 with 12. Sounds weird right?

What these dozenals suggest is that we change to 12 base units. So it takes 12 units to reach the base number. So the number system becomes like this: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, 10.
Essentially adding two more numbers, A and B. Then continuing on we get : 11, 12, 13, 14, 15, 16, 17, 18, 19, 1A, 1B, 20 etc. So what we know as 24 becomes 20 for instance. Creating a new number system known as duodecimal or dozenal.

You see 10 units is a completely arbitrary amount. There is nothing divine or intrinsic about 10 that means we should organise the world like this, it just what we have chosen as our base number. We could organise numbers in base 7, base 2 like they do in binary or even base 600 if you wanted to.

It’s awkward to get your head around I know. You have to conceptualise 10 as somehow now being 12 and 12 now being ten. This YouTube video by Numberphile explains it in more detail…

Alternatively, this odd exert from the 70s show Schoolhouse Rock by Bob Dorough. Explains the duodecimal system in a weird story about an alien with 12 toes. Side note: it’s a little creepy.

Why is 12 better?

Well, a lot of the universe is organised in 12s.

12 months in a year

12 hours on a clock

12 zodiac signs

Western music has 12 notes in an octave

There is something really special about it. Think about the words we use for numbers themselves.
One, two, three, four, five, six, seven, eight, nine, ten, eleven, twelve…then suddenly we switch to thirteen.
We have unique names for the first twelve numbers and then we start recombining one to nine with -teen and then twenty etc.

For me personally, I have always felt an oddly strong affinity for the number 12. When any multiple of twelve comes up in maths question, it makes me a little happy. It is number on my basketball jersey I pick every year and at the end of every one of my passwords that require two numbers and a capital.

I like twelve because it’s easily divided by lots of numbers. It has eight factors (1,2,3,4,6,8,12) compared to 10, which has only four (1,2,5,10). So when dividing 12 or multiples of 12 you more likely end up with rational numbers. Not awkward long fractions or ugly recurring decimal.

That’s the rationale behind duodecimal. Working in a base-12 number system would be easier for calculating fractions, understanding time and for children to conceptualise maths.

For instance, 10 not being neatly divisible by 3 can be annoying in everyday math. For instance, say you go out for dinner with 2 friends and the bill racks up to $80. You go to split it three ways and it ends up at 26.66667.

If you were in the base-12 system,
$80 would be $68 and divided by 3 would come to $22.80 – a far nicer number.

The French’s fault?

Historically we did actually use more of a base-12 number system. Before the French Revolution introduced metric, we used imperial measurements. Which include more 12 based units e.g. 12 inches in a foot and 12 English pence in a shilling. That’s why we still have unique words for 11 and 12 in English.

Though there are all sorts of weird and wonderful counting systems throughout the world. There are regions in New Guinea that use base-27, counting their body parts. In Danish, they use a mix of base-10 and base-20 but then when they get to 50 they start using fractions so the word for 50, halvtreds, means 2̷½ x 20.

In Defence of 10

Though the argument for base-10 and why it so universally used is that we have 10 fingers. Making it easy for children to count. Dozenalists do propose we could count the 12 segments on our fingers and use our thumb to point to them.

The duodecimal alternative for finger counting. (The upside down 2 is alternate way of writing A and the reversed 3 is an alternate version of B). Image by mireille from openclipart and edited by Sally Jenkins.